Application of a New Approach to the Computational Solution of a System of Two Non-Linear Partial Differential Equations

摘要

A new method for integrating certain nonlinear partial differential equations is given. This method is applied to a system of two equations, numerical results are provided, including per cent error, and FORTRAN listings are given. The nonlinear partial differential equations U sub t = UU sub x + VU sub y, U(X, Y, O) = F(X, Y); V sub t = UV sub x + VU sub y, V(X, Y, O) = G(X, Y) are similar to those of hydrodynamics, exhibiting shocks, and have a simple representation for the solution. A numerical method of integration is proposed which preserves boundedness and positivity. Time and memory requirements are small. (Author)